The Mac has been logged into the same Apple ID as the iPhone during all testing of this feature. What I discovered is the Mac must have the Wi-Fi turned on in order to establish a location.
Test 1: A couple days ago it couldn't be found use the iPhone Find My or logging into the iCloud app. Then I turned on the Mac Wi-Fi, even though I already had internet connection with Ethernet. The location suddenly appeared on the map. Then I turned the Wi-Fi off, Ethernet is still connected to the internet. And the location got stale and never refreshed afterwards.
Test 2: Today the Mac location couldn't be found while the Mac Wi-Fi is off. While I was logged on to iCloud, with the Mac, I turned the Wi-Fi on, and suddenly the location updated.
This series of positive and negative testing proves that the Wi-Fi on my Mac must be turned on in order to establish a location for iCloud Find My Mac and Find My mobile app. Very bad design.
I am running macOS Catalina Version 10.15.2.
This doesn't make any sense because I use an Ethernet connection for the Mac and I don't want to use the Wi-Fi. I think Apple iOS has a bug, the Find My Mac iCloud app must work with an Ethernet connection alone and should not depend on Wi-fi to establish the location. The Find My mobile should also find the Mac while the Mac is connected to the internet using Ethernet. What if the Mac were stolen and they used an Ethernet connection only? Then the Find My Mac is useless. Please fix it.
Bruce